(1 point) In order to compare the means of two populations, independent random samples of 438 observations are selected from each population, with the following results: Sample 1 Sample 2 T₁ = 50797

The three solutions to the given Inequalities are; -8, -6, -4

We are given the inequalities as;

102 - 73z > 2z + 2

81 + 11z ≥ 1 + z

Let us solve the first inequality;

Rearrange to get;

2z + 73z < 102 - 2

75z <100

z < 100/75

z < 4/3

Let us rearrange the second inequality to get;

11z - z ≥ 1 - 81

10z ≥ -80

z ≥ -8

Thus, the solution in interval notation is;

-8 ≤ x < 4/3

Thus, three solutions to the given Inequalities are;

-8, -6, -4

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In the case above, the option that one need to include in your answer is to Find a common denominator.

When the numerator and denominator of a fraction are known to not have common factor other than 1, then a person can say that the fraction in its simple form or say its in its lowest term.

Since there is a common numerator and the common denominator will be between 10 and 20. Since 10 is less that than 20, the common denominator will be 20 as both can divide it.

Hence, In the case above, the option that one need to include in your answer is to Find a common denominator.

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Answer:

I don't see any attachement or a picture or anything

Step-by-step explanation:

The answer is D

Answer:

The 10 rational numbers are 21/70, 22/70,23/70, 24/70, 25/70, 26/70, 27/70, 28/70, 29/70 and 30/70.

Step-by-step explanation:

Loosely speaking, a rational number is an expression of the form p/q where p and q are integers and q 0.

Answer:

9506

Example:

Multiply the 7 and 8 to get 56.

Since 56 is greater than 9, you'll have to carry the 5.

       5

       9 7

x 9 8

___________

               6

Multiply the 9 and 8 to get 72.

And, add the carried 5 to get 77.

77 is greater than 9, but there are no more digits to carry over, so just write the 7 down in front.

   7  5

       9 7

x 9 8

___________

       7    7   6

Multiply the 7 and 9 to get 63.

Since 63 is greater than 9, you'll have to carry the 6.

       6

       9 7

x 9 8

___________

       7    7   6

             3   0

_____________

Multiply the 9 and 9 to get 81.

And, add the carried 6 to get 87.

87 is greater than 9, but there are no more digits to carry over, so just write the 8 down in front.

   8  6

       9    7

x 9    8

___________

       7    7   6

  8   7    3   0

_____________

Then add 776 + 8730 to get your answer which is 9506! :)

  1    1

      7   7  6

+  8  7  3  0

_________

    9  5  0  6

Answer:

9.99

Step-by-step explanation:

7.15+2.84

Total ways can 4 seniors and 2 juniors be chosen to participate in a charity event is 1,91,100.

There are 16 seniors and 15 juniors in a particular social organization and

4 seniors and 2 juniors had to be chosen to participate in a charity event.

Combinations are selections made by taking some or all of a number of objects, irrespective of their arrangements. The number of combinations of n different things taken r at a time, denoted by \(^nC_r\) and it is given by,                   \(^nC_r = \frac{n!}{r!(n-r)!}\) , where 0 ≤ r ≤ n.

Therefore the total ways that 4 seniors and 2 juniors be chosen to participate in a charity event = \(^{16}C_{4}.^{15}C_{2}\)

= \(\frac{16!}{4!(16-4)!}$\times \frac{15!}{2!(15-2)!}\)

= 1820 × 105

= 1,91,100

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The complete question is:

There are 16 seniors and 15 juniors in a particular social organization. In how many ways can 4 seniors and 2 juniors be chosen to participate in a charity event?

The Laplace domain equation X(s) is found to be X(s) = (s + 2)/(s^2 + 5s + 6). The time domain equation x(t) can be obtained by applying the inverse Laplace transform to X(s), resulting in x(t) = e^(-t) - e^(-2t).

Given the Laplace domain equation X(s), we need to substitute the given parameters and find its expression in terms of s. The equation provided is X(s) = (s + 2)/(s^2 + 5s + 6).

To obtain the time domain equation x(t), we need to apply the inverse Laplace transform to X(s). The inverse Laplace transform of X(s) will give us x(t) in terms of t.

Applying the inverse Laplace transform to X(s) involves finding the inverse transform of each term separately. The inverse Laplace transform of (s + 2) is simply 1, representing the unit step function. The inverse Laplace transform of (s^2 + 5s + 6) is e^(-t) - e^(-2t), which can be obtained through partial fraction decomposition.

Therefore, the time domain equation x(t) is given by x(t) = e^(-t) - e^(-2t), where t represents time.

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The  Trigonometric Identity sin² x + cos²x = 1 is: A. Pythagorean Identity.

The Pythagorean Identity which  tend to asserts that for every angle x, the sum of the squares of the sine and cosine of x is equal to one  is known as or called a  trigonometric identity.

The  Pythagorean identity can be expressed as:

sin² x + cos² x = 1

This identity is crucial to understanding trigonometry and tend to have several uses in numerous branches of science and engineering.

Therefore the correct option is A.

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Step-by-step explanation:

We can make 2 equations as follows:

2x = y + 16 and x + 2y = 18

x + 2y = 18 is the same as x = 18 - 2y. Hence, 2(18 - 2y) = 2x = y + 16.

2(18 - 2y) = y + 16

36 - 4y = y + 16

5y = 20

y = 4.

Answer:

26 units

Step-by-step explanation:

The distance between two points with coordinates

n²-25

Expand the polynomial using the FOIL method. (A handy way to remember how to multiply two binomials. It stands for "First, Outer, Inner, Last")

Answer:

n² - 25

Step-by-step explanation:

(n - 5)(n + 5)

Each term in the second factor is multiplied by each term in the first factor, that is

n(n + 5) - 5(n + 5) ← distribute parenthesis

= n² + 5n - 5n - 25 ← collect like terms

= n² - 25

The measure of angle 6 is 38°.

What are vertically opposite angles?

Vertically opposite angles are pairs of angles formed by two intersecting lines that are opposite to each other and share the same vertex but are not adjacent angles.

When two lines intersect, they form four angles at the intersection point. The vertical opposite angles are the pairs of angles that are opposite to each other and are not adjacent angles.

We know that, if two lies are parallel and a transversal cuts the lines.

then, the angle formed are corresponding angles ad the vertically opposite angles formed will be equal.

similarly, In the give figure,

we ca see that angle 6 ad angle 38 are vertically opposites angle.

so, angle 6 = 38°

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Answer:

C

Step-by-step explanation:

First, let us clarify what (11, 0) represent

(x, y) ---> (11, 0)

The values are as followed:

x = 11

y = 0

If the problem states that x is the number of days after the promotion started, then it will be 11 days.

When we assert that it has been 11 days, we rule answers A and D.

If the problem states that y is the number of free coffee samples that remain after 11 days (because x is included in this statement), then it will be 0 samples.

Therefore, the answer will be C. After 11 days of the promotion, there will be 0 samples that are left.

Answer:

C

Step-by-step explanation:

Therefore, the coordinates of the terminal points are: (0, 1),(-√2/2, -√2/2) ,(-1/2, -√3/2)

A coordinate is a set of numerical values that uniquely determines the position of a point in space. In two-dimensional space, a coordinate is typically represented by a pair of numbers (x, y), where x represents the horizontal distance from a reference point, and y represents the vertical distance from the same reference point. In three-dimensional space, a coordinate is represented by a triplet of numbers (x, y, z), where x, y, and z represent the horizontal, vertical, and depth distances from the reference point, respectively.

by the question.

Pi/2 is an angle in radians, and it corresponds to an angle of 90 degrees in degrees. The terminal point for this angle lies on the positive y-axis and has coordinates (0, 1).

315 degrees is an angle in degrees, and it corresponds to an angle of 7π/4 radians in radians. To find the terminal point for this angle, we can use the unit circle. Starting from the positive x-axis (the initial side), we rotate 315 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 5π/4 radians. The terminal point lies in the third quadrant and has coordinates (-√2/2, -√2/2).

240 degrees is an angle in degrees, and it corresponds to an angle of 4π/3 radians in radians. To find the terminal point for this angle, we can again use the unit circle. Starting from the positive x-axis (the initial side), we rotate 240 degrees counterclockwise until we hit the terminal side. This corresponds to a rotation of 4π/3 radians. The terminal point lies in the third quadrant and has coordinates (-1/2, -√3/2).

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Answer:

1 mile = 0.5 cm

Step-by-step explanation:

I hope this helps!

Hey again!

The answer to your question is 2 cm = 1 mile

We can solve this by doing 9/4.5, and we get 2. This means that every 2 centimeters in the scale drawing is equal to 1 mile in the actual.

Hope this helps!

(a) The position vector in component form for the polar coordinates (12.6 m, 140°) is (x, y) = (12.6 m * cos(140°), 12.6 m * sin(140°)). (b) The position vector in component form for the polar coordinates (3.60 cm, 40.0°) is (x, y) = (3.60 cm * cos(40.0°), 3.60 cm * sin(40.0°)). (c) The position vector in component form for the polar coordinates (24.0 in., 200°) is (x, y) = (24.0 in. * cos(200°), 24.0 in. * sin(200°)).

x`To obtain the expressions in component form for the position vectors with the given polar coordinates, we can use the following conversions:

For a polar coordinate (r, θ), where r is the magnitude and θ is the angle counterclockwise from the positive x-axis:

The x-component is given by: x = r * cos(θ)

The y-component is given by: y = r * sin(θ)

Let's calculate the expressions for each part:

(a) Polar coordinates: (12.6 m, 140°)

x-component: x = 12.6 m * cos(140°)

y-component: y = 12.6 m * sin(140°)

(b) Polar coordinates: (3.60 cm, 40.0°)

x-component: x = 3.60 cm * cos(40.0°)

y-component: y = 3.60 cm * sin(40.0°)

(c) Polar coordinates: (24.0 in., 200°)

x-component: x = 24.0 in. * cos(200°)

y-component: y = 24.0 in. * sin(200°)

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Answer:

two complex solutions

Step-by-step explanation:

positive= two real

0= one real

negative= two complex

Based on quantitative reasoning, Alden should take the classes from Dr. Baeno in his next semester.

Quantitative Reasoning Behind Choosing Dr. Baeno

Alden talked to 17 friends that previously took course from Dr. Alvarez.

Eight out of 17 friends recommended Dr. Alvarez.

∴ The fraction of his friends in favor of Dr. Alvarez = 8/17

Also, Alden talked to 18 friends who took course from Dr. Baeno.

Eleven out of 18 friends recommended Dr. Baeno.

∴ The fraction of his friends in favor of Dr. Baeno = 11/18

Making Comparison

Now, since we know that,

11/18 > 8/17

The capacity for using knowledge and mathematics to address problems in the real world is known as quantitative reasoning.

Hence, applying quantitative reasoning, we can infer that it is more favorable for Alden to take classes from Dr. Baeno.

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We have shown that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

To show that cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ, and c>0, we will use the CDF method:

1. Define the transformation: Let Y = cX be a function of the random variable X, where c > 0.

2. Find the CDF of Y: We want to find P(Y ≤ y), which is equal to P(cX ≤ y) or P(X ≤ y/c).

3. Express CDF of Y in terms of X: Since P(X ≤ y/c) is the CDF of X at y/c, we have FY(y) = FX(y/c).

4. Find the PDF of X: The exponential distribution has the PDF fX(x) = λ * exp(-λx) for x ≥ 0.

5. Differentiate the CDF of Y to find its PDF: To find fY(y), we differentiate FY(y) with respect to y. Using the chain rule, we have:

fY(y) = d(FX(y/c))/dy = fX(y/c) * (1/c)

6. Substitute the PDF of X: Now, we replace fX(y/c) with its exponential form λ * exp(-λ(y/c)):

fY(y) = (λ * exp(-λ(y/c))) * (1/c)

7. Simplify the expression: fY(y) = (λ/c) * exp(-λ(y/c))

This is the PDF of an exponential distribution with parameter λ/c. Therefore, cX is exponential with parameter λ/c when X is an exponential random variable with parameter λ and c > 0.

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Answer:

D: 187 °F

Step-by-step explanation:

You need to subtract -53 from 134.  But since that 53 degrees is negative and you are subtracting it, you change the negative sign to a positive sign and add positive 53 to positive 134 to get 187.

Answer:

5.1

Step-by-step explanation:

When dividing or multiplying numbers, the answer should have the same amount of significant figures as the number in the problem with the least amount of sig figs.

In the problem 65.8 ÷ 13 ...

65.8 has 3 sig figs

13 has 2 sig figs

13 has THE LEAST AMOUNT OF SIGNIFICANT FIGURES

So, this means the answer must have the same number of sig figs as 13.

Let's round 5.0615384615 to TWO significant figures

the 6 in the number must be rounded up!

Final answer: 5.1

5.1 has  TWO sig figs like the number 13

The value of df for a test with four categories and a sample of any size is 3.

The degrees of freedom (df) for a chi-square test for goodness of fit is calculated as (number of categories - 1) since one category can be determined from the frequencies of the other categories.

In this case, there are four categories, so the degrees of freedom would be (4 - 1) = 3.

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By obtaining a database of every driver in the city of Columbus and calculating the average age, the researcher is analyzing the entire population. Therefore, option c is correct.

In statistics, a population refers to the entire group of individuals or objects that the researcher is interested in studying. In this case, the population consists of every driver in the city of Columbus.

To calculate the average age of drivers in Columbus, the researcher would need data on the age of every driver in the city. If the researcher obtains a database of every driver and calculates the average age based on that data, they are analyzing the entire population.

By obtaining a database of every driver in the city of Columbus and calculating the average age, the researcher is analyzing the entire population. This means that the average age obtained would be a characteristic of the entire population of drivers in Columbus. The researcher would not be dealing with a sample or a subset of drivers, but rather the complete population of interest. Therefore, the correct answer is c. population.

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Let the two expressions are 6a + 12b - 15c and -2a + 2b + 8c. First, subtract the second expression from the first:

Now, subtract them in the reverse order, subtract the first from the second:

The second result is the negative of the first result.

Now, if the results are added then we get the answer zero.

Thus, we can say that when the expressions are subtracted in the opposite order, the results are negative of each other and when the results are added, we get zero as the answer.

Answer:

It is a ratio, which could mean yes and no, mattering which side of the ratio the number goes to.

Step-by-step explanation:

Answer:

yes because it is the same

Nastya's annual payments on the loan will be approximately $7,350.68 (rounded to the nearest cent).

To find Jean's equity as a percent of the house value, we need to calculate the equity and divide it by the house value, then multiply by 100 to get the percentage.

Jean's equity is the difference between the house value and the mortgage amount. So, the equity is $792078.31 - $600,000 = $192,078.31.

To calculate the percentage, we divide the equity by the house value and multiply by 100: ($192,078.31 / $792078.31) * 100 = 24.26%.

Therefore, Jean's equity as a percent of the house value is 24.26%.

Now, let's move on to Nastya's question.

To calculate Nastya's annual payments on a fully amortizing loan, we need to use the formula for calculating the monthly payment:

P = r * PV / (1 - (1 + r)^(-n))

Where:
P = Monthly payment
r = Monthly interest rate (annual interest rate / 12)
PV = Present value of the loan
n = Total number of payments

Given:
PV = $622,422
Annual interest rate = 5.2%
n = 10 years

First, we need to convert the annual interest rate to a monthly interest rate: 5.2% / 12 = 0.43333%.

Next, we substitute the values into the formula and solve for P:

P = (0.0043333 * 622422) / (1 - (1 + 0.0043333)^(-10))

Using a calculator, we get P ≈ $7,350.68.

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The probability of event C given that event A did not occur is 4/52 ÷ 1/36 = 27/52.

a. There are 52 possible outcomes for drawing one card and 6 x 6 = 36 possible outcomes for rolling 2 dice, so the total number of possible outcomes is 52 x 36 = 1,872.

b. The probability of drawing a number greater than 6 is 10/52 (there are 16 cards that meet this criteria: 4 Kings, 4 Queens, and 8 Jacks).

c. The probability of rolling a 7 with two dice is 6/36 or 1/6.

d. Since A and B are independent events, we can multiply their probabilities to find the probability of both events occurring: P(A and B) = P(A) x P(B) = (10/52) x (1/6) = 5/156.

e. To find P(A or C), we add the probabilities of the two events and then subtract the probability of their intersection, since drawing a Queen also satisfies the condition of event A: P(A or C) = P(A) + P(C) - P(A and C) = (10/52) + (4/52) - (1/52) = 13/52 = 1/4.

f. A and B are independent events, since drawing a card has no effect on the probability of rolling two dice.

g. A and C are dependent events, since drawing a Queen affects the probability of drawing a number greater than 6.

h. If event A does not occur, it means that a card less than or equal to 6 was drawn. Since there are 36 possible outcomes for rolling 2 dice and only 1 of them results in a 7, the probability of event B occurring is 1/36. Given that event A did not occur, the probability of event C is simply the probability of drawing a Queen, which is 4/52. Therefore, the probability of event C given that event A did not occur is 4/52 ÷ 1/36 = 27/52.

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The radius of the circle is approximately 10.17 units (rounded to two decimal places).

To find the radius of the circle, we need to use the formula that relates the central angle to the length of the arc and the radius of the circle. The formula is given as:

arc length = radius x central angle

In this case, the arc length is given as 24.4 and the central angle is given as 2.4 radians. Substituting these values in the formula, we get:

24.4 = r x 2.4

Solving for r, we get:

r = 24.4 / 2.4

r ≈ 10.17

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